Optical phase measurement method and system

ABSTRACT

A measurement system for use in measuring parameters of a patterned sample, the system including a broadband light source, an optical system configured as an interferometric system, a detection unit, and a control unit, where the interferometric system defines illumination and detection channels having a sample arm and a reference arm having a reference reflector, and is configured for inducing an optical path difference between the sample and reference arms, the detection unit for detecting a combined light beam formed by a light beam reflected from the reflector and a light beam propagating from a sample&#39;s support, and generating measured data indicative of spectral interference pattern formed by spectral interference signatures, and the control unit for receiving the measured data and applying a model-based processing to the spectral interference pattern for determining one or more parameters of the pattern in the sample.

TECHNOLOGICAL FIELD

The present invention is generally in the field of optical measurementtechniques, and relates to an optical system and method for determiningparameters and/or properties of a patterned sample utilizing phasemeasurements, particularly useful in semiconductor industry.

BACKGROUND

The constant progress in semiconductor technology demands for thefabrication of ever smaller devices. This development has to beaccompanied by concurrent improvement in metrology capabilities, inorder to monitor and control the fabrication process.

Over the last few decades, optical critical dimension (OCD) metrologyhas taken a pivotal role in semiconductor manufacturing process, due toits extreme sensitivity, accuracy, flexibility and speed. In order toprovide adequate improvement of the metrology capabilities, OCD toolshave gone through extensive improvement and refinement, and can providetoday extremely accurate broadband spectral measurements and extremelyhigh throughput.

In addition to the process of improving the basic tool characteristics,another venue by which OCD performance can be improved is throughdiversifying the measured information. Commonly measured opticalproperties are the reflectivity for different incidence angles,azimuths, polarizations and wavelengths. In addition, the relative phasebetween reflected TE and TM polarization components can be accessedthrough (e.g.) ellipsometric measurements.

Another important attribute of light scattered from a patternedstructure is its spectral phase. This quantity describes the relativephase between the incident and reflected electromagnetic waves.Typically, this phase has different values for different wavelengths,incident angles\azimuths and polarizations.

Since accessing the phase directly is not possible at opticalfrequencies, one has to use interference effects, usually observed withan interferometer, and recover the encoded phase information from theinterference effects. Most interferometers consist of a split opticalpath that is recombined to form interference fringes. One arm of thepath is kept as a reference, and the other interacts with the sample.The interference signal from these two components is then used toextract the spectral phase.

U.S. Pat. No. 6,985,232 describes a phase-sensitive interferometericbroadband reflectometer for optically inspecting and evaluating asubject. According to this technique, a broadband optical beam is splitinto probe beam and reference beam portions; the probe beam is directedto be reflected by the subject; after the probe beam has been reflectedby the subject, the probe beam and the reference beam are rejoined. Thelength of the path traveled by the probe beam or the reference beam ismodulating within a predetermined range during the measurements. Then,spectroscopic analysis of the rejoined beams is performed on aper-wavelength basis at a selected set of points within thepredetermined range.

General Description

There is a need in the art for a novel phase measurement technique,which allows effective measurement with desirably high signal-to-noiseratio in the measured signal. Also, it might be desired to have ameasurement system eliminating or at least significantly reducing arequirement to movement of the elements of an optical system.

The present invention provides a novel system and method for spectralphase measurements, by providing a spectral interferometric system,where a spectral interference pattern is detected by a spectral sensorand is in the form of multiple (at least two) spectral interferencesignatures corresponding to different (at least two) optical pathdifferences (OPDs) between the sample and reference arms. In someembodiments, such spectral interferometric system utilizes across-polarization based measurements, by using polarization filteringin the illumination and detection channels. In some embodiments of theinvention, spectral interference pattern (multiple spectral signatures)is obtained using a single exposure (single measurement) at arbitraryz-position, i.e. arbitrary distance between the optical paths of areference light beam and a probe light beam interacting with the sample.In this connection, the following should be understood:

As indicated above, spectral phase can be measured using interferometricmeasurements. Traditional interferometry techniques require tightcontrol of a path length difference in order to achieve accuratemeasurement results. In homodyne interferometers (such as phase shiftinterferometry), full retrieval of phase information requires asuccession of measurements (at least 3 successive measurements), usingseveral path length phase shifts. This usually requires a sequentialmeasurement process, and measurement accuracy is compromised by setupinstability during the sequence. These challenges also carry over towhite-light interferometers. Also, commonly used techniques based on aswept source, vertical/phase scanning, and multi-z technique, typicallyuse a sequential measurement process:

Achieving adequate system stability in a wafer metrology tool is an evengreater challenge due to the following additional factors. Usually, suchsystems require high speed motion for sampling wafers at multiple pointswith high throughput. This adds heavy, high-precision machineryoperating at high accelerations and velocities to the system with theirassociated problems, such as vibrations, settling times, air-flow andturbulence, and heating and cooling cycles. In addition, wafers arerelatively large samples, complicating matters even further due to thelarge frame that has to straddle the wafer. This exposes the system tohigher sensitivity to short-term effects, such as vibrations andturbulence, as well as long-term effects such as thermal expansion andchuck contamination. Finally, the wafer stack diversity and variabilityintroduces shifts in absolute height (z) measurement from the wafer (forboth optical and capacitive sensors), adding undesirable complexity tothe system.

In view of the above, it might be desirable to have an interferometerthat allows full spectral phase retrieval using a single exposure atarbitrary Z values.

The present invention deals with several of the main difficulties ofusing broadband (‘white light’) and/or phase-shift interferometry formeasuring the spectral phase, in order to perform OCD and thin filmmetrology, as well as material optical properties investigation.

The present invention provides effective calibration schemes and dataanalysis methods. As will be described more specifically further below,specific calibrations can be used to account for dominant system-relatedeffects on the measured signal. For spectral phase measurements, thereis a freedom in choosing what measured property to use in order toextract the required data. The inventors have shown that by correctchoice of the quantity to be compared with the calculations, it ispossible to significantly improve sensitivity, and obtain a robustmeasurement.

The present invention also provides algorithmic approaches to accountfor system-related effects in the analysis of spectral reflectometrydata. For example, the inventors have shown how vibrational sensitivity,which is one of the main factors limiting usability of interferometricmethods, can be accounted for using correct algorithmic treatment.

As indicated above, the present invention provides for constructing aunique implementation of spectral phase measurement, based onwhite-light interferometer that allows obtaining the full spectralphase, using cross-polarization scheme and/or a single exposure atarbitrary z (dimension along the optical axis). The single exposurerenders the system immune to transient instability effects thatcompromise sequential measurements. As is common in most white-lightinterferometers, the height ambiguity of a single measurement can becompensated for by performing a mathematical transformation on themeasured data (such as unwrapping), and/or by prior-knowledge ofestimated value of the height. Since in the field of OCD the structureunder examination is usually known up to some variability in itsdimensions, this prior knowledge is mostly available. The inventionprovides several methods to achieve single-exposure phase measurement(which can be expanded with additional measurements as required). Thesemethods include spectrographic white-light interferometry; spectralheterodyne white-light interferometry; position-dependent spectral whitelight interferometry.

The invention also provides a method for spectral phase measurementbased on several interferometric measurements. In this case, speciallydesigned algorithms are used to extract an accurate phase by taking intoaccount several data sets and efficiently canceling noise effects. Thesemeasurements can be taken at different optical path differences (OPD's)or during a z scan.

The invention includes a measurement scheme enabling an interferometricmeasurement at many OPDs simultaneously and by that achieving betternoise cancelation.

In addition to the measurement methods, the invention provides severalalgorithmic methods enabling accurate and robust analysis of themeasured data. These methods can be specifically tailored to thechallenges imposed by the interferometric measurements.

The processing of the measured data includes fitting procedure betweenthe measured data and a theoretical model. Typically, the fittingprocess includes merit function definition. The merit function is ameasure of the degree of fit between calculated (theoretical) andmeasured data. The merit function may be the RMS error betweenmeasurement and calculation data pieces, where each of the measurementand calculation data pieces is in the form of reflected intensity I andphase ϕ simultaneously. For example, each of the reflected intensity andphase may be a function of the wavelength(s) used in the measurements,polarizations and incident\reflected angles. Other types of data can bepresented and interpreted e.g. complex electric field components orsin/cos of the measured phase.

As interferometry provides the most straightforward method for phasemeasurement, one of the methods of the invention described belowinvolves using time-dependent measurements for this purpose. Thisapproach bypasses many of the difficulties introduced by interferometricmeasurements.

The invention thus provides spectral phase measurement for OCDapplications. The technique of the invention can be specifically usedfor CD measurements, as compared to the traditional interferometry whichis typically used only for thickness and z related measurements. Thepresent invention utilizes the spectral nature of the phase extractionor a so-called “interferometric spectrum”. The technique of theinvention provides a model based solution for spectral phasemeasurements, as well as polarized spectral phase measurements, andallows for combining spectral phase measurements with regular SpectralReflectometry (SR). The measurement technique of the invention canadvantageously be incorporated in automatic optical inspection (AOI)system, utilizing normal and/or oblique incidence mode.

Thus, according to one broad aspect of the invention, there is provideda measurement system for use in measuring parameters of a patternedsample, the system comprising: a broadband light source; an opticalsystem configured as an interferometric system; a detection unit; and acontrol unit; wherein the interferometric system defines illuminationand detection channels having a sample arm and a reference armcomprising a reference reflector, and is configured for inducing anoptical path difference between the sample and reference arms; thedetection unit comprises a configured and operable for detecting acombined light beam formed by a light beam reflected from said reflectorand a light beam propagating from a sample's support, and generatingmeasured data indicative of spectral interference pattern formed by atleast two spectral interference signatures; and said control unit isconfigured and operable for receiving the measured data and applying amodel-based processing to the spectral interference pattern fordetermining one or more parameters of the pattern in the sample.

In some embodiments, the interferometric system comprises polarizers inthe illumination and detection channels.

The interferometric system comprises a mechanism for inducing theoptical path difference (OPD) between the sample and reference arms. Insome embodiments, such OPD inducing mechanism comprising a driving unitfor controllably moving either one or both of the reflector and thesample's support along an optical axis of the interferometric system,while both the reflector and sample are oriented perpendicular to theoptical axis.

In some other embodiments, such OPD mechanism is implemented without aneed for moving the reflector and/or sample. This can be achieved byorienting at least one of the sample's support and the reflector with afixed tilted position with respect to the optical axis of theinterferometric system. In another example, the OPD mechanism isimplemented by inducing defocusing effect on illuminating light beampropagating along the reference arms towards the reflector, e.g. bylocating the reflector in a plane parallel to and spaced-apart from afocal plane of an objective lens unit of the interferometric system. Yetanother example for implementing the OPD mechanism without any movingelement is by configuring the reflector as a retro-reflector assembly.

In some embodiments, the light source is configured and operable forproducing illumination in the form of ultra short pulses.

According to another broad aspect of the invention, there is provided anoptical system for use in measuring parameters of a patterned sample,the optical system being configured as a spectral interferometric systemdefining illumination and detection channels having a sample arm and areference arm comprising a reference reflector, and being configured forinducing an optical path difference between the sample and referencearms, such that combined light beam, propagating along the detectionchannel to a spectrometer, is formed by a light beam reflected from saidreflector and a light beam propagating from a sample and is indicativeof spectral interference pattern formed by at least two spectralinterference signatures corresponding to at least two optical pathdifferences.

According to yet another broad aspect of the invention, it provides amethod for use in measuring parameters of a patterned sample, the methodcomprising:

directing broadband light through an interferometric optical systemhaving a sample arm and a reference arm with an optical path differencebetween the sample and reference arms;

detecting a combined light beam formed by a light beam reflected from areflector in the reference arms and a light beam propagating from thesample under measurements, and generating measured data indicative ofspectral interference pattern formed by at least two spectralinterference signatures; and

applying a model-based processing to the spectral interference patternand determining one or more parameters of the pattern in the sample.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to better understand the subject matter that is disclosedherein and to exemplify how it may be carried out in practice,embodiments will now be described, by way of non-limiting examples only,with reference to the accompanying drawings, in which:

FIG. 1A schematically illustrates a measurement system of the inventionconfigured as a spectral interferometer system;

FIGS. 1B and 1C schematically illustrate two more examples of themeasurement system of the invention utilizing tilted field (tiltedmirror or sample);

FIG. 1D illustrates interference pattern detected by the 2D sensor;

FIGS. 2A to 2D and 3A to 3C illustrate the principles of differentimplementations of the optical path difference (OPD) control between theoptical paths of the probe and reference beams, where FIGS. 2A and 3Aexemplify the configuration and spectrogram for tilted field embodimentutilizing tilting of the reference mirror or the sample, FIGS. 2B and 3Bexemplify the configuration and spectrogram for defocused reference beamembodiment, and FIGS. 2C-2D and 3C exemplify the configuration andspectrogram for the use of retro-reflector;

FIG. 4 illustrates interferometric and non-interferometric spectra;

FIGS. 5A to 5C show the phase calibration of measured data forinterferometric spectra at two z positions (FIG. 5A), difference betweenthe fitted and measured spectra (FIG. 5B), and optimized phase functioncharacterizing the optical system (FIG. 5C);

FIG. 6 shows an example for structural parameters obtained by spectralinterferometry of the invention;

FIG. 7 shows the measured spectra recorded from grating of Silicon-Oxidelines on a Silicon wafer (˜1800 Å line width, 1800 Å trench width, 3000Å line height);

FIG. 8 illustrates a low-frequency signal (‘Envelope’) multiplied by aCW carrier, providing the heterodyne signal;

FIG. 9 illustrates the simulation results (calculated heterodyneinterference signal) for the interference spectrum from a perfect mirrorsample and reference;

FIG. 10 illustrates the heterodyne scheme, showing bandwidth-limitedsignal (top) which occupies a region in frequency space (‘z’ in thiscase) than the carrier (bottom);

FIG. 11 shows the heterodyne detection in z space;

FIG. 12 illustrates practical difficulties with implementing heterodynemethodology;

FIG. 13 shows the sampling of the signal of interest by a 3-phasecarrier;

FIG. 14 shows coherence function in z space for a diffraction limitedinterferometer and a simple grating; and

FIGS. 15A and 15B show, respectively, the effect of tilting the sampleand/or reference mirror, creating the position-dependent fringes, andthe effect of using hack focal plane (BFP) imaging, combined withdefocusing of the sample/reference mirror.

DETAILED DESCRIPTION OF EMBODIMENTS

Reference is made to FIG. 1A schematically illustrating an example of ameasurement system of the invention, which is configured as a spectralinterferometer system operable to measure spectral phase of lightreturned (reflected and/or scattered) from a patterned structure (e.g.semiconductor wafer) to enable determination of the parameters of thepattern.

It should be noted that in this specific but not limiting example ofFIG. 1A, as well as examples of FIGS. 1B and 1C described below, thesystem is exemplified as being configured for operation with the normalincidence mode and bright field measurement mode. It should, however, beunderstood that the invention is not limited to this configuration, andgenerally, measurement can be obtained in any (oblique or other)angle-of-incidence mode, as well as can utilize dark-field measurementmode or a combination of bright- and dark-field measurement modes.Moreover, as will be described below with reference to FIG. 1A, thesystem may implement polarization-based dark-field measurement modewhile having a principle normal-incidence bright-field configuration.

The measurement system is based on a general spectral reflectometerconfiguration, where sample reflectivity is accurately measured, butbeing modified to utilize the interferometric measurements according tothe invention. More specifically, the measurement system, generallydesignated 10 in FIG. 1A, includes a light source 14 providing broadbandinput light L_(in) (white light) including probe and reference lightbeams L_(p) and L_(r) accordingly, a detection unit 16; and an opticalsystem 20 configured as light directing arrangement for directing lightfrom the light source 14 towards a sample/structure under measurementslocated on a sample's support 12 and a towards an optical pathdifference inducing mechanism 28 (planar mirror in this example) anddirecting returned light to the detection unit 16.

In the example of FIG. 1A, such a planar mirror is located in a planeperpendicular to the optical axis of the optical system 20 (i.e.“untilted mirror”), and may or may not be movable along the opticalaxis. Also, in the example, of FIG. 1A, the detection unit 16 includesspectrometer (spectrophotometer) 19B for generating spectral data oflight incident thereon, and also optionally includes an imaging detector19A for navigating to measurement sites on the structure. Output of thedetection unit 16 is communicated (via wires or wireless signalcommunication) to a control unit 30.

The optical system 20 is configured for defining an illumination channelfor propagating input light L_(in) from the light source 14 towards thestructure plane 12, and a detection channel for propagating light beingmeasured L_(meas) to the detection unit 16. The input light L_(in) is tobe split into probe and reference beams L_(p) and L_(ref), and lightbeing measured L_(meas) includes reflection (scattering) L′_(p) of theprobe beam L_(p) from an illumination region on the structure 12 andlight L_(r) reflected from a reference mirror 28.

The optical system 20 includes a beam splitter/combiner 22 which isconfigured for spatially separating between input light L_(in) and lightbeing measured L_(meas), and an objective lens unit 24 (one or morelenses). In the present example of system configuration, which usesnormal incidence and bright-field detection modes, these units 22 and 24are located in both the illumination and detection channels. The lightdirecting arrangement 20 also optionally includes a collimating lens 21in the illumination channel, being in the optical path of input lightL_(in) propagating from the light source towards the beam splitter 22,and a tube lens 23 in the detection channel, being in the optical pathof measured light propagating to the detection unit.

The optical system 20 further includes a beam splitter/combiner 26 whichsplits the input light L_(in) into the probe and reference beams L_(p)and L_(r) and directs them respectively along the sample arm towards thestructure 12 and along a reference arm towards the reference mirror 28.Mirror 28 reflects the reference beam L_(r) hack to the beamsplitter/combiner 26 where it is combined with reflection (scattering)L′_(p) of the probe beam L_(p) from an illumination region on thestructure 12 into a combined light beam L_(meas) to bemeasured/detected. The combined light beam propagates to the detectionunit 16, i.e. passes through the objective 24 and beams splitter 22 andfurther via the tube lens 23 which focuses it onto the spectrometer 19Bof detection unit 16.

According to the invention, in this example of FIG. 1A, the opticalsystem 20 includes polarizers 32 and 34 located in respectively,illumination and detection channels. More specifically, input lightL_(in) on its way from the light source 14 passes through the polarizer32 and a specifically polarized (e.g. linearly polarized) input light(L_(in))_(pol) is directed by beam splitter/combiner 26 to objective 24which directs it to beam splitter/combiner 26. The latter splitspolarized input light (L_(in))_(pol) into probe and reference polarizedbeams L_(p) and L_(r) and directs them to respectively the structure onsupport 12 and reference mirror 28. Reflections from the structure andmirror L′_(p) and L_(r) are combined by beam splitter/combiner 26 into acombined light beam L_(meas) having said specific polarization, whichpasses through the objective 24 and beam splitter 22 to the polarizer34, which allows only light of said specific polarization(L_(meas))_(pol) to propagate to the detection unit. This combinedpolarized light beam is divided by beam splitter 29 into light portions(L_(meas))₁ and (L_(meas))₂ which are directed to respectively theimaging detector 19A and spectral sensor (spectrometer) 19B. Thespectrometer 19B measures every wavelength's intensity separately andaccordingly measured data generated by the spectrometer corresponds tothe spectral interference pattern. The system 10 also includes a drivingunit 33 associated with either one or both of the mirror 28 and thesample's support 12 for controllably moving it/them along the opticalaxis, i.e. z-axis, thereby inducing optical path difference resulting intime variation of the spectral interference pattern. It should beunderstood that using polarizers 32 and 34 accommodated and oriented asdescribed above actually provides a cross-polarization scheme, whichresults in the dark-field measurement mode. It should be understood,that when the mirror 28 is not used (i.e. is moved out of the opticalpath of incident light or is inactivated by the use of an appropriateshutter), the system 10 can operates as a spectral reflectometer.Accordingly, the same system 10 may be shifted between two differentoperational modes, as a spectral interferometer and spectralreflectometer.

Control unit 30 is typically a computer system including inter alia suchutilities (software/hardware) as data input and output utilities 30A,memory 30B, data processor 30C, and an optical path differencecontroller 30D. Also optionally provided in the control unit is acalibration utility 30E, as will be described further below.

Reference is now made to FIGS. 1B-1D showing some other examples of thespectral interferometer system of the invention. To facilitateunderstanding, the same reference numbers are used for identifyingcomponents that are common in all the examples. In these non limitingexamples, the spectral interferometric system utilizes a differentprinciple for inducing optical path difference, while utilizingstationary mounted components of the system, i.e. mirror and/or sample'support are maintained at fixed positions, but is/are tilted withrespect to the optical axis (tilted field). It should be noted that thistilted field approach can be combined with the above describedpolarization-based configuration of the illumination and detectionchannels.

Thus, a system 100 of the example of FIG. 1B is configured generallysimilar to that of FIG. 1A, but the optical system 120 in system 100 isdifferent from optical system 20 of system 10 in that untilted movableor stationary mirror 28 used in optical system 20 is replaced in opticalsystem 120 by a tilted mirror 128. Also, in figure FIG. 1B an imagingsensor (19A in FIG. 1A) is not shown, and accordingly beam splitter (29in FIG. 1A) is also not shown. As indicated above, although polarizersare not shown in FIG. 1B, they may be used in system 100. System 200shown in FIG. 1C is configured generally similar to system 10 of FIG. 1Ain that it includes two detection channels defined by the imaging andspectral sensors, and optical system 220 (light directing arrangement)includes the beam splitter 29. However, this system 200, similarly tothat of FIG. 1B, has tilted mirror 128. In the example of FIG. 1C,polarizers (not shown) may or may not be used.

Further, in system 100 (FIG. 1B) and system 200 (FIG. 1C), the detectionunit 16 includes a 2D spectrometer 18. Accordingly, the optical systems120 and 220, in examples of FIGS. 1B and 1C respectively, includecylindrical tube lenses 123 and 223 and diffraction gratings in thespectrometer detection channel, as specifically illustrated in FIG. 1Cwhile not being shown in FIG. 1B.

Thus, according to some embodiments of the invention, exemplified inFIGS. 1B and 1C, the optical path difference (OPD) between the opticalpaths of the probe and reference beams L_(p) and L_(r) is createdwithout movement of any optical element. This is achieved by providingone of the following stationary mounted arrangement: (1) tilted mirroror tilted sample's support; (2) inducing defocusing effect on thereference beam, e.g. by positioning the untilted mirror n a planespaced-apart from a focal plane (plane conjugate to the focal plane ofthe objective); or (3) inducing a field shift to the reference beam,i.e. tilted pupil/displaced field, by configuring the mirror as aretro-reflector assembly (flips).

In the examples of FIGS. 1B and 1C, the tilted planar mirror embodimentis illustrated. This and other options will be described in more detailsfurther below.

Thus, input light L_(in) from the light source 14 is split between thesample arm and the reference arm where the tilted mirror 128 is located.Light L_(r) reflected from the reference mirror 128 is combined withlight reflection L′_(p) from the sample in the beam combiner 26 anddirected to the detection unit. As more specifically shown in FIG. 1C,the spectral sensor 18 is a 2D sensor, and portion (L_(meas))₂ of thecombined light beam L_(meas) that is directed to the spectral sensor,preferably propagates through the cylindrical tube lens 223 anddiffraction grating 36. Signals corresponding to different OPDs, due totilt of the stationary reference mirror 128 are detected by the 2Dsensor along one axis, whereas the other axis is a spectral signalrepresentation. Since the mirror 128 is tilted and the sample is nottilted, every interference line occurs at different OPD similar tointerference with additional z scan. It should be understood that thesame would be obtained if the planar mirror is not tilted (i.e. isperpendicular to the optical axis) while the structure is located on atilted support, i.e. OPD is induced in reference path or measurement oneby tilt of mirror or sample. An interference pattern is presented inFIG. 1D.

It should be noted that the mirror tilt is calibrated in advance, andaccordingly the spatial axis on the spectrograph is fully calibrated andevery line represents a known OPD. It should also be noted thatinterferometric measurements are highly sensitive to vibrations, andinterferometer systems that utilize multiple z measurements suffer fromdrifts and vibration changes between consecutive measurements. Using theprinciples of the above described embodiments of the invention (i.e.obtaining z-scan without moving the mirror in the reference arm),provides a more stable spectrograph scheme, since all z measurements aretaken at the same time (single image) thus share drifts and vibrations.

Reference is made to FIGS. 2A-2D and FIGS. 3A-3C illustrating theprinciples of the three different implementations of the optical pathdifference (OPD) control between the optical paths of the probe andreference beams.

As shown in the example of FIG. 2A, tilting the reference mirror or thesample (or, generally, tilted field) creates the OPD (along the Z-axis,or optical axis of the system) determined as:Δz=x·tan θwherein θ is the tilt angle, and x is the corresponding dimension in thesample plane.

Turning back FIGS. 1B and 1C, this configuration provides fringes linearin field, whereatan(l/FOV)·θ=1 Fringe

FIG. 3A shows the measured spectrogram (top) and the effect of phase inthe shifts of cross fringes (bottom) for the Tilted Field Shearconfiguration of FIG. 2A.

In the example of FIG. 2B, where defocused reference beam is used, theOPD is determined as:Δz=h·cosθ=h·(1-S ²)^(1/2)wherein S=sinθ, and h is the defocus.

FIG. 3B shows the measured spectrogram (top) and the effect of phase inshifts of spectral fringes (bottom) for the Defocus Pupil Shearconfiguration of FIG. 2B.

The configurations of FIGS. 2C and 2D provide that S is uniform inpupil, and linear fringes along pupil are obtained:l/2NA·Shift=1 FringeNA being a numerical aperture, and the OPD is determined as:Δz=S·Δx,where Δx is the defocus.

FIG. 3C shows the measured spectrogram (top) and the effect of phase inshifts of cross fringes (bottom) for the Tilted Pupil Shearconfiguration of FIGS. 2C and 2D.

As can be seen, the field shear configuration (FIG. 2A) seems to be thesimplest option. Defocus shear configuration (FIG. 2B) can operate withsmaller Δz (less spectral fringes) if high NA objective is used. In thepupil shear configuration (FIGS. 2C and 2D), any deviation from idealfringe form (linear or Fresnel) can be used to estimate the phasevariation in NA.

Generally, the signal measured with the spectral interferometer is givenby|I _(k)(p,z)^(2=F) _(Ω{|S) _(k)(p,Ω)+R _(k)(Ω)·exp(ikz)|²}  (1).where S_(k) (p) is the complex electric field reflected from the sample,R_(k) is the electric field reflected from the reference mirror, and kis the wave vector. The fields are functions of the wave vector(magnitude and direction) and of the sample's parameters p (such asstructure, thickness, optical properties etc.). The symbol Ω constitutesvarious system parameters, such as the optical numerical aperture,polarization, vibrations, optical aberrations etc. The function F_(Ω)denotes the mathematical operation for summing over the various systemparameters Ω.

As seen in equation (1), the interferometric signal |I_(k) (p, z)|depends not only on the sample parameters p but rather on the opticaldistance, z, between the sample and the reference mirror.

FIG. 4 exemplifies interferometric and non-interferometric spectra. Theinterferometric spectra, S⁽¹⁾ _(int) and S⁽²⁾ _(int) are measured usingthe interferometric spectrometer setup for respectively different samplepositions z₁ and z₂ along the optical axis, and the non interferometricspectra S⁽¹⁾ _(int) and S⁽²⁾ _(int) are measured for respectively thesample and the reference, while blocking one of the interferometer arms.As can be seen in the graphs, when positioning the sample at differentlocations (Z₁, Z²) with respect to the reference mirror, the signalchanges significantly.

The reference reflectance R_(k) is complex, and can be rewritten asR _(k) =|R _(k)|·exp(iφ _(k)),where φ_(k) is referred to as the “calibration phase”.

In order to correctly analyze the signal reflected from a measuredtarget, it is first essential to accurately characterize the amplitudeand phase of the reference mirror. The amplitude |R_(k) can be found forexample by simply removing the sample from the system, thus equation (1)reduces to the square of the mirror amplitude reflectance (curve R_(non)in FIG. 4). The calibration phase, however, is hidden in such ameasurement. The phase calibration may be performed by placing a wellcharacterized sample in the system (such as bare Silicon) and measuringthe interference signal. In this connection reference is made to FIG.5A-5C, showing the phase calibration of measured data forinterferometric spectra at two z positions (FIG. 5A), difference betweenthe fitted and measured spectra (FIG. 5B), and optimized phase functioncharacterizing the optical system (FIG. 5C).

More generally, it is possible to control properties of the referencemirror, so as to optimize the metrology performance. As will bedescribed below, the interference signal sensitivity depends on therelative phase between the sample and the reference mirror, as well ason their relative amplitudes. It is possible to change the mirrormaterial\structure for optimal performance, and/or to obtain severalmeasurements, with the mirror reflectivity being appropriately changed(e.g. using a mirror with printed pattern, and rotating it so as tochange its reflectivity).

In order to extract the calibration phase from such measurements, theinventors considered the difference between the measured spectra andcalculated spectra (theoretical, model-based data) as follows:M _(k)(φ_(k) ,z)=F _(Ω{|S) _(k)(Ω)+|R _(k)(Ω)|·exp(iφ_(k))·exp(ikz)|^(2}−|I)(z)|²  (2)where |I (z)|² are measured spectra and the termF _(106 {/S) _(k)(Ω)+/R _(k)(Ω)/·exp(iφ _(k))·exp(ikz)/²}of the equation is calculated according to the known reflectance of thesample, reference mirror, and the integration operator. An optimizationalgorithm can be used to find the phase function φ_(k) and z positionssuch that |M_(k)(φ_(k), z)| is minimized

It is possible to use a single measurement at one z position, or variouspositions for noise reduction or better optimization.

This approach can be extended to several calibration targets for bettercalibration and optimization. Such approach can be especially importantin order to allow accurate calibration for the full spectral range.

FIG. 5B shows the error spectrum M_(k) (φ_(k), z) for the optimizingfunction which is shown in FIG. 5C. Indeed, once this function isassumed to characterize the phase induced by the optical system, theresidual error is negligible.

It is important to note that in the calibration step it is possible toinsert more fitting parameters to the optimization on M_(k) such thatvarious system parameters are introduced to the integration operatorF_(Ω){ }. These can include the system vibration profile, the numericalaperture, spectral smearing and de-coherence, calibration sample andmirror parameters, etc.

Let us consider a sample (e.g. semiconductor sample) measured by thespectral interferometer, to obtain its structural (geometrical andoptical properties) parameters (i.e. OCD metrology). As noted above, themeasured signal is given by|I _(k)(p,z)|^(2=F) ₁₀₆ {|S _(k)(p,Ω)+R _(k)(Ω)·exp(ikz)|²}  (3)where R_(k) (Ω) and F₁₀₆ are now completely characterized by calibrationmeasurements (either as described above or other suitable technique).Various merit functions (MF) can now be defined which can be optimizedin order to obtain the structural parameters p (CD, heights, side wallangles, thickness, material properties, etc.) characterizing themeasured sample. An example for such function is given by:

$\begin{matrix}{{{M_{Ispect}( {p,z} )} = {\sum\limits_{k}{{{F_{\Omega}\{ {{{T_{k}( {p,\Omega} )} + {{{R_{k}(\Omega)}} \cdot {\exp( {i\;\varphi_{k}} )} \cdot {\exp({ikz})}}}}^{2} \}} - {{I( {p,z} )}}^{2}}}}},} & (4)\end{matrix}$where T_(k)(p,Ω) is the calculated complex reflectance of the giventarget sample.

As in any OCD metrology procedure, this merit function MF is used as ameasure for ‘goodness of fit’ between the calculated (theoretical) andmeasured spectra. Once the application parameters which provide the bestfit condition (minimal MF) are found, they are identified as thosecharacterizing the measured sample. The search for the set ofapplication parameters providing the best fit condition, as well as theoptimized definition of merit function MF, can be based on thealgorithmic approaches used for OCD, as described for example inWO2011/104713, assigned to the assignee of the present application andincorporated herein by reference. Alternatively, as will be describedbelow, the merit function definition can be altered to improverobustness against noise and convergence accuracy.

While for standard OCD, commonly used merit function involve RMS errorbetween calculation and measurement, in the case under considerationhere there is additional flexibility in its definition. A possiblealternative (more advanced) merit function is the normalized, so calledcosine merit function, and is given by:

$\begin{matrix}{{{M_{\cos}( {p,z} )} = {\sum\limits_{k}{{{{CT}_{k}( {p,z} )} - {C_{k}(z)}}}}},} & (5)\end{matrix}$where

$\begin{matrix}{{{{CT}_{k}( {p,z} )} = \frac{\begin{matrix}{{F_{\Omega}\{ {{{T_{k}( {p,\Omega} )} + {{{R_{k}(\Omega)}} \cdot {\exp( {i\;\varphi_{k}} )} \cdot {\exp( {i\; k\; z} )}}}}^{2} \}} -} \\{{S_{k}}^{2} - {R_{k}}^{2}}\end{matrix}}{2{S_{k}}{R_{k}}}}{{C_{k}(z)} = \frac{{{I_{k}(z)}}^{2} - {S_{k}}^{2} - {R_{k}}^{2}}{2{S_{k}}{R_{k}}}}} & (6)\end{matrix}$

It is possible to define a general merit function which includes variousmerits and various measurements at more than one z position:

$\begin{matrix}{M_{total} = {\sum\limits_{i}{\alpha_{i}{M_{i}(z)}}}} & (7)\end{matrix}$

Reference is made to FIG. 6 which shows an example for structuralparameters obtained by spectral interferometry of the invention. This isan example of SiO₂ on Si measurements (a blank Silicon wafer with a thinSilicon-Oxide (˜2963 Å thickness). Here, the non-interferometricspectrum (curve S_(non)) is shown together with the interferometricspectrum (curve S_(int)) and the so called Cosine spectrum (curveS_(norm)) being the normalized cosine spectrum C _(k)(z) in equation 6,are shown, where solid and dashed curves correspond to respectivelymeasured and calculated spectra. When using the correct Oxide thicknessand z position, the theoretical spectra match the measured ones. It isevident that by optimizing the spectral differences it is possible toobtain the Silicon-Oxide thickness and the z position.

The above mentioned merit functions are only few examples out of manypossibilities. It is also possible to use the spectral phase extractedfrom interferometric measurements or the components of the measuredcomplex field (real and imaginary parts). These entities can be comparedto their modeled counterparts and used to find the sample's structuralparameters.

More complex applications, which are customary in the semiconductorindustry (including non-blanket samples), can be measured and analyzedas well. Reference is made to FIG. 7 which shows the measured spectrarecorded from grating of Silicon-Oxide lines on a Silicon wafer (˜1800 Åline width, 1800 Å trench width, 3000 Å line height). In the figure,solid and dashed curves correspond to measured and calculated spectra,and curves S_(non), S_(int), and S_(norm) correspond to, respectively,non-interferometric spectrum, interferometric spectrum and normalizedcosine spectrum (C_(k) Z) in equation 6). Here again, when using thecorrect structural parameters (Oxide thickness, line spacing, line widthand z position), the theoretical spectra match the measured ones.

Instead of using a spectrometer to measure the interference signal foreach wavelength separately, it is possible to measure the interferenceon an achromatic detector (such as CCD camera) and repeat themeasurement while scanning the optical distance between the sample andreference (z). Similar approach is used for white light interferometer[Griffiths, P.; de Hasseth, J. A. (18 May 2007). Fourier Transform

Infrared Spectrometry (2nd ed.). Wiley-Blackwell. |SBNO-471-19404-2|,where spectral information in the IR is obtained by multipleinterferometric measurements, varying the reference arm length.

In order to analyze this situation, the optical signals of the sampleand reference can be considered accordingly as pulses in the time domainAS(t), R(t). A shift in the optical path difference between referenceand sample is denoted by a temporal shift τ. Since the detector can beoperated to integrate over the total pulse width, such measured signalis given by:P(τ)=·|S(t)+R(t−τ)² dt=∫|S(t)² dt+∫|R(t)² dt+S⊗R*+c.c  (8)and using Fourier transform:{tilde over (P)}(ω)=∫|S(t)|² dt+∫|R(t)|² dt+{tilde over (S)}(ω)·{tildeover (R)}*(ω)+c.c  (9)where ω=2πc/λ is the angular frequency.

From the quantity {tilde over (P)} (ω) it is possible to obtain thecomplex sample reflectance {tilde over (S)} (ω) since it includes twooffset terms (∫|S(t)|²dt, ∫|R(t)|²dt) and the reference function {tildeover (R)}* (ω) which can be measured beforehand.

This measurement method actually presents the Fourier conjugate of theabove-described spectral interferometry. The spectral axis in thespectral interferometry is replaced here by a spatial axis (z).

Once the complex reflectance {tilde over (S)} (ω) is obtained, the abovedescribed methods, i.c. Merit function optimization, can be used.

The above described novel approach of the spectral interferometry can beused for accurate spectral phase measurement, following the principle ofheterodyne measurement. The principle of heterodyne measurement aregenerally known and need not be described in details, except to note thefollowing. The heterodyne concept can be considered as a method forencoding the amplitude and phase of a complex-valued signal using only areal-valued signal. An outline for the procedure is as follows: thesignal is multiplied by high frequency constant-wave (CW) carrier (aswill be described more specifically further below) and the real part istaken to generate the heterodyne signal; the envelope of the heterodynesignal is the amplitude of the original signal; and the shift of theheterodyne signal relative to the carrier is the phase of the originalsignal.

FIG. 8 illustrates this concept, showing a low-frequency signal(‘Envelope’) multiplied by a CW carrier, and providing the heterodynesignal. Both the amplitude and phase of the original signal can bederived from the heterodyne result.

In a white-light interferometer, the spectrum of unbalanced armsacquires a CW component e^(ikΔz) with frequency proportional to Δz,being the difference in optical path length between the arms. Herek=2π/λ denotes the freespace wave number for light of wavelength λ, andfor simplicity can be assumes that the reference arm is spectrallyneutral. For large enough Δz, this CW component can be used to generateheterodyne signal mixing with the original spectral signal S(k) (complexamplitude and phase) from the sample.

Such large values of Δz can be used to allow the use of heterodyne toolsfor the signal analysis.

Optical intensity measurement generates a product of signal and carrierI(k)=|S(k)+e ^(ikΔz)|²=1+|S(k)|²+2Re {S(k)e ^(−ikΔz)}.  (10)

This equation (10) is similar to Eq. 1 above, but simplified for clarity(Eq. 1 presents the more comprehensive description).

In equation (10), the last term, 2Re {S(k) e^(−ikΔz)}, is the heterodynesignal.

FIGS. 1A-1C show examples of the spectral interferometer enablingspectral heterodyne measurements. A light source 12 used in theinterferometer has a sufficient spectral range to cover the spectralregion of interest. The interferometer includes a beam-splitter unit 22which splits input light into a reference arm L_(ref) and a sample(probe) arm L_(p) that interacts with the sample, and a beam-combiner 26that combines the output of both arms, after the sample arm interactionwith the sample. A control device/mechanism for controlling orgenerating (a fixed or variable) optical path length difference (OPD)between the arms may be implemented using movable untilted mirror 28 orstationary tilted mirror 128). In the spectral interferometer of theinvention shown in FIG. 1A, movement of untilted mirror 28 in thereference arm, or movement of the sample's support 12 is used, ifmeasurement in reflection mode is considered. In the spectralinterferometer of the invention shown in FIGS. 1B and 1C, neither mirrornor sample needs to be moved during the measurements, which is achievedby the above-described tilted or defocused configurations. The OPD is tobe large enough to generate a CW carrier signal e^(ikΔz) with highenough frequency. A spectrometer used for measuring the spectralintensity of the interference signal has suitable spectral resolutionfor correctly sampling the CW carrier signal whilst retaining sufficientcoherence as will be discussed below.

FIG. 9 illustrates the simulation results (calculated heterodyneinterference signal) for the interference spectrum from a perfect mirrorsample and reference. This is the manifestation of the real part of theaforementioned CW carrier signal e^(ikΔz), but the horizontal scale iswavelengths (as opposed to wave numbers), and thus the chirpedappearance.

The results of the measurements can be interpreted in order to extractthe sample's (complex) reflection (both amplitude and phase). Asexemplified in FIGS. 1A-1B, the control unit 30 is appropriatelyconfigured for processing and analyzing measured data indicative of thespectral interference pattern including two or more spectralinterference signatures. This data processing utilizes model basedapproach. The data processor utility 30D includes fitting module. Aswill be described below with respect to the heterodyne detectionalgorithms, direct information on the interference spectrum can be usedto infer metrological data on the sample. However, it should be notedthat in model-based metrology it is possible to generate models thatalready produce spectral interference trial measurements to be comparedagainst the actual measurements. The model based approach providesflexibility of which element of the spectra to use. Using the heterodynedetection algorithm of the present invention, provides insight to therequired working points for the model-based metrology methods, wheremeaningful data may be generated by the measurements.

Traditionally, heterodyne detection is based on the spectral propertiesof the carrier and the bandwidth-limited (BW) signal. More specifically,it is required that they occupy different regions in the frequencyspectrum (z-space, which is conjugate to the wavenumber k in the presentcase). FIG. 10 illustrates the heterodyne scheme, showingbandwidth-limited signal (top) which occupies a region in frequencyspace (‘z’ in this case) than the carrier (bottom).

From Eq. 10 above, for a perfect unit reference, the interference signalis:I=1+|S| ² +Se ^(−ikΔz) +S*e ^(ikΔz),  (11)

A frequency space can be used to separate the 4 components in the abovesum. This, however, requires the CW frequency to be at least 3 times thesignal bandwidth (BW) to avoid aliasing. This is illustrated in FIGS. 11and 12. FIG. 11 shows the heterodyne detection in z space. The lowfrequency signal is multiplied by the carrier signal, creating two sidelobes. As long as these side lobes have no overlap with low frequencycomponent, heterodyning can be implemented with no aliasing errors. FIG.12 shows practical difficulties with implementing heterodynemethodology. The discreteness of the measured signal creates an overlapbetween the signal components in z (frequency) space, leading toaliasing errors.

Then, the third term in eq. 11 is multiplied by the carrier to recoversignalS=(Se ^(−ikΔz))e ^(ikΔz).

However, considering application of this method to spectral measurementsas generated by a white-light interferometer, since the interferencesignal is discretely sampled by the detector, this method is implementedusing discrete Fourier transforms. However, discrete Fourier imageprocessing suffers from spectral leakage: any function of k that isnon-periodic will leak to adjacent bins. This leads to cross-talkbetween the 4 components, contaminating the extracted signal. Ensuringthat the sample's spectrum and carrier e^(ikΔz) are periodic on themeasured k-space window is not practical. Windowing the interferencesignal softens the leakage, but not enough for sensitive metrologyapplications.

In order to overcome the above problems, the invention provides adifferent approach. It should be noted that in homodyne interferometryat least 3 phase shifts are needed for full recovery of signal. Let usconsider the CW carrier as a constantly varying phase shift. Sincesignal is assumed to vary slowly (3BW≤CW), the carrier samples eachsignal information “cell” with at least 3 different phases. This isillustrated in FIG. 13 showing the sampling of the signal of interest bya 3-phase carrier.

Assuming the sample signal can be expressed as a sum of a finite numberof real-valued basis functions ƒ_(kn), n=1, . . . , N, we have:S _(k)=Σ_(n)ƒ_(kn)(a _(n) +ib _(n))  (13)

Possible candidates for suitable basis functions are sines centered on asuitable k-space sampling grid, sine-squared on such a grid, or trianglefunctions (linear 1D finite element shape functions). It should be notedthat the sampling grid needs to be adjusted to match the basis functionbandwidth, i.e. if the spacing between adjacent functions is too largethere will be aliasing problems.

Next, assuming that the sample intensity, |S_(k)|², reference intensity,|R_(k)|², and interference intensity, I_(k), have been measured, wherek=1, . . . , K, the interference intensity is given by:I _(k) =|S _(k)|² +|R _(k)|²+γ_(k)(S _(k) *R _(k) e ^(+ikΔz) +S _(k) R_(k) *e ^(−ikΔz))  (14)where γ_(k)<1 is a decoherence term, possibly from z-jitter, finitecoherence length, detector noise, integration on pupil or field or bothor other degrees of freedom such as polarization, etc.

In order to solve this system of equations, γ_(k) is absorbed into theunknown coefficients, i.e.γ_(k) S _(k)=Σ_(n)ƒ_(kn)(a _(n) +ib _(n))  (15)and then the linear system is solvedΣ_(n)[|R _(k)|cos kΔz ƒ _(zn) |R _(k)|sin kΔz ƒ _(kn][b) _(n) a _(n)]=I_(k) −|S _(k)|² −|R _(k)|²  (16)

Finally, an estimate for decoherence can be extracted, and the solutionis:

$\begin{matrix}{\gamma_{k} = \frac{{\sum_{n}{f_{kn}( {a_{n} + {ib}_{n}} )}}}{S_{k}}} & (17) \\{S_{k} = \frac{\sum_{n}{f_{kn}( {a_{n} + {ib}_{n}} )}}{\gamma_{k}}} & (18)\end{matrix}$

Let us consider degrees of freedom. There are 2N unknown coefficientsand K measurements, yielding the requirement K≥2N. This is a reductioncompared to the expected 3-fold requirement from the classicalheterodyne detection scheme, since the sample intensity |S_(k)|² is alsomeasured.

An advantage of the algebraic method is that it accommodates decoherenceeffects which are hard to control and estimate, and also gives anestimate for their strength. Incorporating the decoherence effects alsoallows accurate reconstruction of the interference signal in order toobtain a solution residue vs. the actual measurement.

The carrier frequency Δz has to be high enough so that the matrix iswell-conditioned and numerically invertible (this is the physicalrequirement that the phase variation has enough samples of each basisfunction ƒ_(kn)). The last requirement may be traded for severalmeasurements at various lags z_(j): each basis function ƒ_(kn) issampled by enough phases due to several Δz_(j). Since solving linearsystem is fast, unknown parameters can be fit, such as fine-tuningΔz_(j) to minimize the solution residue. This allows fitting on multi-zjump inaccuracies with relatively few numerical resources.

It should be noted that as in any spectral measurement, z-ambiguity ine^(ikΔz) means that the spectrum is known only up to a linear phaseterm. In order to compare the detected signal to a given spectrum, oneneeds to perform a gauge-fixing procedure, such as (but not limited to)setting the linear phase term to zero, or considering only the secondderivative of the phase.

It is thus clear that enough basis functions N is required to correctlydescribe the assumed spectral signal S_(k)=Σ_(n)f_(kn)(a_(n)+ib_(n)).This, in turn, requires at least K≥2N measurement points, where thecarrier oscillates enough for each basis function. This means that Δzhas to be large enough so that e^(ikΔz) performs one cycle per basisfunction, and the K sampling points are spaced to correctly sample theinterference signal. However, large Δz causes the interference fringecontrast to decrease, as a function of a coherence length of thespectrometer. For a diffraction limited interferometer with a uniform,simple grating, the coherence function has a triangle shape asillustrated in FIG. 14 showing coherence function in z space for adiffraction limited interferometer and a simple grating, where N is thenumber of grating lines, and n is the diffraction order.

The Fourier transform of the coherence function is the spectralresolution point-spread function (PSF) of the spectrometer:γ(λ,λ′)=sinc²(2πNn(λ−λ′)/λ′)  (19)

Thus, in order to perform heterodyne detection on a spectrum with finedetails, a spectrometer needs to have at least twice the spectralresolution required to correctly sample the spectral intensity, andalso, since high fringe contrast ensures adequate signal-to-noise ratio(SNR) and may also be required to overcome other possible decoherencecauses.

It is possible to bypass the difficulties of interferometric schemes infavor of ultrafast optics techniques. Optical pulses with very shortduration (e.g. femtosecond pulses) contain very broad spectralcomponents. The spectral phase of such pulses is generally of interestand as such, various characterization techniques have been studied [RickTrebino, Frequency-Resolved Optical Gating: The Measurement ofUltrashort Laser Pulses. Springer (2002); Mitsuo Takeda et all.“Fourier-transform method of fringe-pattern analysis for computer-basedtopography and interferometry”. J. Opt. Soc. Am. 72 156 (1982); U.S.Pat. No. 6,611,336]. Most of these techniques make use of non-linearoptical interactions to deduce the spectral phase.

In the present case an ultrafast laser pulse is used where all itswavelengths are phase locked (transform limited pulse). The transformlimited pulsef(t)=∫|F(ω)|·exp(iωt)dωimpinging on the sample is transformed tos(t)=∫S(ω)·exp(iωt)dω.whereS(ω)=|S(ω)|·exp(iφ _(ω)).

The new amplitudes |S(ω)| correspond to the reflectance spectrum of themeasured sample. The relative phases φ_(ω) correspond to the differentphase shifts (optical path differences) induced by the sample to eachfrequency in the pulse. As mentioned, various characterizationtechniques are able to measure the phase function of the reflected pulseand thus to obtain this crucial applicative information without the needof an interferometer.

Turning back to FIGS. 1B to 1C, illustrating the spectral interferometerof the invention, the sample is illuminated by a white light sourcethrough an interferometric objective. The signal is collected and imagedon a spectrograph. The interferometric objective may perform via e.g. anentrance slit, a 1D imaging of the sample on one axis of its 2D CCD, andunfolds the spectrum of each imaging pixel on the other axis of the CCD.

This setup may have many variants enabling the spectral phase of thereflected field to be extracted, depending on the specific method ofextracting the phase, and the ability to assure valid SNR and reduceunwanted system effects.

With the ‘standard’ interferometry, the phase is extracted bymeasurements of the sample and reference reflectivity, and of thecombined interferometric signal. The use of the spectral interferometricsystem of the invention provides for obtaining spectrographic data whichis richer in spatial information, thus enabling averaging, noisereduction and also measurement of spatial variations of the phase.

As described above with reference to FIGS. 1B-1D and 2A, the use oftitling the sample and/or the reference mirror, by introducing a tilt toone of the planes or both of them, creates a constant defocus gradientalong the imaged axis. This in turn produces linear fringes in thefield, caused by the different OPD along the imaged axis. In thisconnection, reference is made to FIG. 15A showing the effect of tiltingthe sample and/or reference mirror, creating the position-dependentfringes. This position dependence can be used for accurate extraction ofthe spectral phase. As the defocus gradient is constant, this will allowbetter fitting of the signal.

As described above with reference to FIGS. 1B-1D and 2B, alternativelyusing hack focal plane (BFP) imaging, combined with defocusing of thesample/reference mirror, by introducing a defocus to one of the planesor both of them, results in Fresnel fringes in the field, caused by thedefocus-dependent phase variation in the NA plane. This is shown in FIG.15B. By fitting to this fringe pattern, the spectral phase can beextracted with high accuracy. This phase variation has a specific,known, functional dependence Since the defocus is a single parameter,imaging the BFP with the spectrograph improves the ability to extractthe spectral phase.

In the above-described methods, the system properties should beconsidered. For instance, in the BFP with defocusing method, there is anadvantage for a larger NA, allowing for defocus sensitivity. Otherwise,large defocus distances must be reached in order for the Fresnel fringesto appear.

Specifically, a system that is designed to measure the angular intensityprofile of a target (such as back focal plane imaging or Dome imaging)can be joined with an interferometer to complement the measured datawith the phase information. Alternatively, a specially designedwave-front sensor (phase detector) can be used to measure the angularintensity and phase without an interferometer. This option includesvarious methods of phase and intensity characterization such as“Coherent Point Microscopy” (CPM) described in WO2014/102792) assignedto the assignee of the present application. The CPM technique providesfor measuring a light intensity pattern from a sample related to theFourier transform of the scattering matrix of a sample and thuscontaining information on both its amplitude and phase. The CPM approachutilizes a combination of an imaging optics in conjunction with coherentlight source with so-called “critical illumination”, i.e. illuminationproviding a range of illumination angles onto the sample and coherentinterference between different illumination angles. This can, forexample, be obtained by directly imaging a point-like source onto thesample under measurements, or alternatively focusing a collimated laserbeam on the sample.

The following are some examples of the measured data interpretation.

Many algorithmic approaches can be devised and optimized forinterpreting the measured spectral phase. The standard approach to OCDspectral interpretation involves comparing the measured spectrum with amodel-based calculation, based on some geometrical description of themeasured structure. Many variations and improvements can be used, in thesame manner as for other OCD-based methods (library-based, real timeregression etc.).

In addition to this approach, it is possible to use a model-lessapproach, where some features in the measured spectrum are correlatedwith some parameter characterizing the application. The correlation canbe obtained through some physical reasoning or after measuring severalsamples of known attributes (i.e. semi-empirically).

It is possible to use this metrology approach in combination with anyother optical or non-optical metrology method. For example, the acquiredinformation can be used in conjunction with spectral reflectometry,spectral ellipsometry, dome scatterometry, CD-SEM data etc. Thesecomplementary datasets can be used to remove correlation betweenparameters. Alternatively, accurate information from one metrologymethod (e.g. top-CD from a CD-SEM) can be injected (as a fixed value)into the interpretation process of the spectral interferometrymeasurement.

As described above, with reference to FIGS. 1B-1D and 2A-2D, thetechnique of the present invention provides for obtaining requiredspectral interferometric data for extracting the structure parametersusing a single measurement. It should be noted that, if needed, thespectral interferometer of the present invention can provide for aso-called multi-z measurements. Measurements can be obtained for severalvalues of sample height (in direction of the optical axis), or fordifferent positions of the reference mirror, and these measurements areused to extract a cleaner phase measurement. As also described above, zmay be used as a fitting parameter, which may be extracted from themeasured spectrum.

The measured spectra can be spanned as a linear combination of somebasis functional set, thus enabling to rephrase the fitting process inthe form of a simple linear problem. The choice of suitable basisfunctions can improve the fit accuracy, as well as robustness to noise.For the multiple types of basis functions, the approach can be extended,using e.g. higher-order finite-element shape functions. Fornon-translationally invariant basis functions, the approach can beextended, using e.g. wavelets, polynomials etc.

Information on the temporal coherence of the signal may be included inthe fitting process. Accounting for this factor will cause some smearingof the interference spectrum, which could be important (especially ifthe spectral resolution is not high). The coherence factors can bereadily estimated based on the optical parameters of the system.Alternatively, it is possible to deduce the coherence factors from ameasurement (one or few), by using the coherence factors as fittingparameters.

Other optical designs of the measurement system can be used, obtainedthrough setups incorporating spectrographs, thus extended the approachof the invention to multi-channel cases.

The measurement system of the invention can use any suitable type oflight source, such as lamp, LED, laser, supercontinuum laser, laserdriven plasma, others, as well as any illumination type such as Kohler,critical, extended vs. point, etc. Any suitable types of beamsplitters/combiners and configurations can be used, such ashalf-silvered plates, cubes, fiber splitter/combiners, planar lightwavecircuit splitter/combiners, as well as polarized beam splitter. Also,separate splitter/combiners can be used (in a Mach-Zehnderconfiguration) or a single splitter/combiner (in a Michelsonconfiguration). A moving beam splitter can be used to alternate betweena standard reflectometry measurement and an interferometric measurement.The detection unit may utilize any spectrometer types and configurationsincluding the option to use a spectrograph to obtain heterodyne spectralmeasurements in multiple parallel channels (such as, but not limited to,sample cross-section, scattered pupil cross-section), and/or use of asecond spectrometer to obtain a measurement of the interferometercombiner's “rejected” channel, and/or use of an additional spectrometerto concurrently obtain pure intensity (non-interferometric) measurementsfrom the sample. The measurement technique of the invention may utilizepolarized or unpolarized light, as well as different illumination andcollection polarization states during measurements (including variouscross-polarization measurements). The optical path length control may beimplemented using fixed path length difference, mirrors,retroreflectors, spatial light modulators, liquid crystals, MEMS, etc.,as well as control of either the sample path or reference path or both.A MEMS reference mirror can be used to control the OPD and tilts of theinterferometer. Also, any suitable scheme of the optical interactionwith sample can be used, such as transmission or reflection ordouble-pass through sample (with a mirror/reflector behind sample),normal and/or oblique illumination and collection angles, oblique atvarious azimuths, optically resolved or unresolved sample, apodizedillumination/collection apertures.

The optical components may also be of any suitable known type, such asobjectives of high or low NA, either custom or existing, optimized forlaser illumination and/or for broad band, reflective or refractive.Different configurations are possible for the interferometry element,such as Michelson, Mirau, Linnik It is also possible to reduce noisesand non-linearity by extending number of measurements (in different z,or other). Changes could be applied in Fourier plane (such as Phasecontrast), or Fourier filtering could be used.

The technique of the invention can be related and combined with otheroptical techniques, e.g. CPM, in case Bertrand lens is used, of directlyobtaining spectral phase in Fourier plane (as described in WO2014/102792assigned to the assignee of the present application and incorporatedherein by reference). Measurements of spectral phase can similarly beintegrated into a more comprehensive OCD metrology scheme, implementingother information channels. For example, the spectral phase measurementcan accompany an angular phase measurement technique, either as anadditional measurement unit, additional measurement head or even adifferent channel in the same metrology head.

What is claimed is:
 1. A measurement system for use in measuringparameters of a patterned sample, the system comprising: a broadbandlight source; an optical system including an objective lens andconfigured as an interferometric system; a detection unit; a controlunit; and a beam-splitter-and-combiner positioned along an optical pathbetween the objective lens and the patterned sample, wherein theinterferometric system defines an illumination channel, and detectionchannels having a sample arm and a reference arm comprising a referencereflector, wherein the sample arm is not parallel with the referencearm, the detection channels comprise a first detection channel and asecond detection channel that share at least the objective lens; and isconfigured and operable to induce an optical path difference between thesample arm and reference arm, and to combine output of the sample armand reference arm into the detection channels for propagation of acombined light beam formed by a light beam reflected from said referencereflector and a light beam propagating from the patterned sample, thelight beams derived from light originating from the broadband lightsource, wherein the detection unit comprises an imaging sensor and aspectral sensor, the spectral sensor is configured and operable todetect a first portion of the combined light beam from the firstdetection channel and generate measurement data indicative of eachwavelength of the first portion of the combined light separately, theimaging sensor is configured to detect a second portion of the combinedlight beam; wherein said control unit is configured and operable toreceive the measurement data for determining one or more parameters of apattern in the patterned sample, and wherein thebeam-splitter-and-combiner is configured to: split the light originatingfrom the broadband light source into a probe light beam and a referencelight beam, direct the probe light beam along the sample arm towards thepatterned sample, and direct the reference light beam along thereference arm towards the reference reflector.
 2. The measurement systemof claim 1, wherein said interferometric system comprises polarizers,wherein the polarizers consist of a first polarizer in the illuminationchannel and outside the collection channels a second polarizer in thedetection channels and outside the illumination channel.
 3. Themeasurement system of claim 2, wherein said interferometric systemcomprises a driving mechanism, associated with either one or both ofsaid reference reflector and a sample support supporting the patternedsample, and configured and operable to controllably move at least one ofsaid reference reflector and the sample support along an optical axis ofthe interferometric system, to induce the optical path differencebetween the sample arm and the reference arm.
 4. The measurement systemof claim 1, wherein at least one of said reference reflector and asample support supporting the patterned sample is oriented with a fixedtilted position with respect to an optical axis of the interferometricsystem, providing the optical path difference between the sample arm andthe reference arm.
 5. The measurement system of claim 4, wherein saidreflector is located in a plane parallel to and spaced-apart from afocal plane of an objective lens unit of said interferometric system. 6.The measurement system of claim 4, wherein said reflector is configuredas a retro-reflector assembly.
 7. The measurement system of claim 1,wherein said interferometric system is configured and operable to inducedefocusing effect on an illuminating light beam propagating along thereference arm towards said reference reflector, providing the opticalpath difference between the sample arm and the reference arm.
 8. Themeasurement system of claim 1, wherein the broadband light source isconfigured and operable to produce illumination in the form ofultra-short pulses.
 9. The measurement system of claim 1, comprising anadditional beam-splitter-and-combiner that is configured to split thecombined light beam to the first portion of the combined light beam andto the second portion of the combined light beam.
 10. The measurementsystem of claim 9, wherein the imaging sensor is a CCD.
 11. Themeasurement system of claim 1, wherein the reference reflector is a MEMSreference mirror that is movable for controlling at least one of tiltand the optical path difference.
 12. The measurement system of claim 11,wherein the imaging sensor is in communication with the control unit.13. A method for use in measuring parameters of a patterned sample, themethod comprising: directing broadband light through an interferometricoptical system, the interferometric optical system including anobjective lens and defining an illumination channel and detectionchannels having a sample arm not parallel to a reference arm comprisinga reference reflector; the detection channels comprise a first detectionchannel and a second detection channel that share at least the objectivelens; splitting the broadband light into a probe light beam and areference light beam, wherein the splitting is performed along anoptical path between the objective lens and the patterned sample;directing the probe light beam along the sample arm towards thepatterned sample; directing the reference light beam along the referencearm towards the reference reflector; inducing an optical path differencebetween the sample arm and the reference arm; combining output of thesample arm and reference arm into the detection channel for propagationof a combined light beam formed by a light beam reflected from saidreference reflector and a light beam propagating from a patternedsample, the light beams derived from the broadband light; detecting anintensity of every wavelength separately of a first portion of thecombined light beam using a spectral sensor and generating measurementdata, detecting, by an imaging sensor that differs from the spectralsensor, a second portion of the combined light sensor; and determiningfrom the measurement data one or more parameters of a pattern in thepatterned sample.
 14. The method of claim 13, wherein the referencereflector is a MEMS reference mirror, the method further comprisingmoving the MEMS reference mirror.
 15. The method of claim 13, andfurther comprising controllably moving, along an optical axis of theinterferometric system, at least one of said reference reflector and asample support supporting the patterned sample, thereby inducing theoptical path difference between the sample arm and the reference arm.16. The method of claim 13, and further comprising orienting, with afixed tilted position with respect to an optical axis of theinterferometric system, at least one of said reference reflector and asample support supporting the patterned sample, thereby providing theoptical path difference between the sample arm and the reference arm.17. The method of claim 16, and further comprising positioning saidreflector in a plane parallel to and spaced-apart from a focal plane ofan objective lens unit of said interferometric system.
 18. The method ofclaim 16, and further comprising configuring said reflector as aretro-reflector assembly.
 19. The method of claim 13, and furthercomprising inducing a defocusing effect on an illuminating light beampropagating along the reference arm towards said reference reflector,thereby providing the optical path difference between the sample arm andthe reference arm.
 20. The method of claim 13, and further comprisingproducing illumination of the broadband light in the form of ultra-shortpulses.